Usually means: Space compact near each point.
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We found 4 dictionaries that define the word locally compact:

General (2 matching dictionaries)
  1. locally compact: Wiktionary
  2. Locally compact: Wikipedia, the Free Encyclopedia

Science (2 matching dictionaries)
  1. Locally Compact: Eric Weisstein's World of Mathematics
  2. locally compact: PlanetMath Encyclopedia

Definitions from Wiktionary (locally compact)

adjective:  (topology) Of a topological space: such that, for every point of the space, there is a neighborhood of that point whose closure is compact.

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